He also forecast that other countries would follow Britain's lead in voting to leave the European Union.
"Brexit is going to end up being a great thing," Trump on yesterday said of Britain's referendum vote last June to leave the European Union.
The president-elect said a trade deal with Britain would be "good for both sides".
"Absolutely, very quickly. I'm a big fan of the UK, we're gonna work very hard to get it done quickly and done properly," said Trump, confirming he will meet British Prime Minister Theresa May soon after his inauguration on January 20.
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Trump also said Brexit would likely be followed by others in the 28-country bloc deciding to leave.
"I think people want . . . Their own identity, so if you ask me ... I believe others will leave," Trump said, following Britain's June vote to leave the EU.
The president-elect blamed the referendum result on an influx of refugees to Europe, which saw more than a million people arrive during 2015.
Trump campaigned on an anti-immigration platform during the presidential race, promising voters he would build a war on the Mexico border to stop people entering the US illegally.
Focusing on refugees in Europe, Trump said their arrival could lead to the break-up of the EU.
"I do think keeping it (the EU) together is not gonna be as easy as a lot of people think," he said.
Trump was interviewed for The Times by Michael Gove, a writer and MP from Britain's ruling Conservative Party who was a leading figure in the anti-EU campaign.
The president-elect has previously allied himself with another leading Brexit campaigner, Nigel Farage, the former leader of the UK Independence Party who flew to the US to support Trump during his election bid.
Farage was the first British politician to meet with Trump following the November election, a move which prompted frustration within the British government which has long since clashed with anti-establishment Farage.
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